Elliptical copulas exhibit radial symmetry, where the distributions of
\((U_i,U_j)\)  and \((1-U_i,1-U_j)\)  are the same.
Yet there are applications where this is unrealistic,
including for the dependence between equity returns [1]}, [2]} and regional
electricity spot prices [3]}. The implicit copulas of
skew elliptical distributions [4]} allow for
asymmetric pairwise dependence, with the most common
being those constructed from the differing skew \(t\)  distributions.
[5]} were the first to construct an implicit copula from a skew \(t\)  distribution (i.e. a “skew \(t\)  copula”),
for which they used a special case of the generalized hyperbolic distribution,
and [6]} do so for an adjustment of the skew normal distribution
of [7]}.
The most popular variants of the skew \(t\)  distribution are those of [8]} and [9]},
which
share a similar conditionally Gaussian representation.
[3]} show how to construct
implicit copulas from these latter two
skew \(t\)  distributions, and estimate them using MCMC.
[11]}
considers maximum likelihood estimation for the skew \(t\)  copula constructed
from the distribution of [8]}, and [13]} consider a dynamic extension of the
skew \(t\)  copula of [5]} for high dimensions.
